2.7 Shuffle algorithm

Derived data structure and algorithm analysis--c language description Exercise 2.7

In a function int rand (int n) returns a random number between 1-n. How do I get the array a[n] scrambled?

The initial fisher–yates algorithm is to open an array b[n], put the intended a[n] into b[n], the steps are as follows

Set i=0

1. Generate a random number between 1-a.length length K

2, put a[k] to b[i], remove the a[k],i++ in the array A.

3, if a.length>0, go to the 1th step.

The algorithm is to remove the number in a, each time to shift, so the algorithm complexity of O (n^2).

For example an algorithm process is as follows:

Random number Range	Random number	A	B
		1 2 3 4 5 6 7 8

Random number Range	Random number	A	B
1–8	3	1 2 3 4 5 6 7 8	3

Random number Range	Random number	A	B
1–7	4	1 2 3 4 5 6 7 8	3 5

Random number Range	Random number	A	B
1–6	5	1 2 3 4 5 6 7 8	3 5 7
1–5	3	1 2 3 4 5 6 7 8	3 5 7 4
1–4	4	1 2 3 4 5 6 7 8	3 5 7) 4 8
1–3	1	1 2 3 4 5 6 7 8	3 5 7 4 8 1
1–2	2	1 2 3 4 5 6 7 8	3 5 7 4 8 1 6
		1 2 3 4 5 6 7 8	3 5 7 4 8 1 6 2

Later the algorithm has improved, not another array, but to exchange array A above the elements to achieve rearrangement.

This algorithm has 2 versions, the same principle:

Version 1:

[CPP]View Plaincopy

1. for (int i = n; i>=1;-I.)
2. {
3. int J=rand (i); //Generate a random number between 1-i
4. Exchange (A[i],a[j]); //Exchange A[i],a[j]
5. }

Version 2:

[CPP]View Plaincopy

1. for (int i = 1; I <= n; ++i)
2. {
3. int j= (rand (n)/N) * (n-i+1) +i-1; //Generate a random number between i-n
4. Exchange (A[i],a[j]); //Exchange A[i],a[j]

A calculation process for version 1 is as follows:

Modern Method[edit]

We ' ll now do the same thing using Durstenfeld's version of the Algorithm:this time, instead of striking out the chosen Nu Mbers and copying them elsewhere, we ' ll swap them with the last number is not yet chosen. We ll start by writing out the numbers from 1 to 8 as before:

Roll

Range		Scratch	Result
		1 2 3 4 5 6 7 8

For your first roll, we roll a random number from 1 to 8:this time it's 6, so we swap the 6th and 8th numbers in the list:

Roll

Range		Scratch	Result
1–8	6	1 2 3 4 5 8 7	6

The next random number we roll from 1 to 7, and turns off to be 2. Thus, we swap the 2nd and 7th numbers and move on:

Roll

Range		Scratch	Result
1–7	2	1 7 3 4 5 8	2 6

The next random number we are from 1 through 6, and just happens to be 6, which means we leave the 6th number in the list ( Which, after the swap above, was now number 8) in place and just move to the next step. Again, we proceed the same the until the permutation is complete:

Roll

Range		Scratch	Result
1–6	6	1 7 3) 4 5	8 2 6
1–5	1	5 7 3 4	1 8 2 6
1–4	3	5 7 4	3 1 8) 2 6
1–3	3	5 7	4 3 1 8 2 6
1–2	1	7	5 4 3 1 8 2 6

Reference: Http://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle

2.7 Shuffle algorithm